On Dec 22, 2008, at 3:56 PM, Nils Bruin wrote: > On Mon, Dec 22, 2008 at 10:23 AM, Robert Bradshaw > > <rober...@math.washington.edu> wrote: >>> On Dec 22, 2008, at 6:20 AM, John Cremona wrote: >> >>>> You can do K(r.lift()), but it would be nicer if this was >>>> handled by >>>> coercion magic. >> >>> This isn't really a coercion issue per se, it's a question of adding >>> another case to the _element_constructor_ method of number >>> fields. Do >>> we want coercion here, i.e. should someone be able to write r + >>> K.gen >>> ()? If so, would it be the most natural to put the result into K or >>> the quotient ring? > > I am not sure that the result of r + K.gen(), if allowed at all, > should end up in K or in R. > > An alternative interpretation: r is an element of an algebra over Q. > We add to it an element of K, which is a base extension of Q. > Shouldn't the result end up in the base extension of R by K over Q? An > advantage of this interpretation is that it does not depend on > R and K being isomorphic (which may be non-trivial to determine. Do R > and K have pointers to each other?), so can apply more generally. > > According to Bradshaw's coercion in towers of extensions, It seems the > question should be resolved depending on the names of the generators > of K and R, > which could be problematic if the generators of R and K have the same > name (as in this example), but not the same defining polynomial (not > the case in this example). Perhaps a reason to not extend the coercion > model to non-free extensions by default, or introduce a clear rule?
Personally, I don't think this is "natural" enough to happen automatically, and as mentioned above is rather ambiguous (would a base extension be preferable? certainly more consistant). However, K (r) should be fixed to work. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
